# Research

## Summary

Our research mostly revolves around the field of mesoscopic conductors and superconductors. This includes graphene and topological aspects of condensed matter physics, such as topological insulators and superconductors, and Majorana bound states, as well as spintronics and the effects of disorder. Numerical simulations play a large role in our work, and we work on developing new algorithms applicable in our research activities. More information on a few topics is given below.

Much of what we do is covered in this online course. Check it out.

For a more systematic listing of our activity, check out our recent publications.

## Research topics

**Majorana bound states.** One example of an exotic physical object that is
simple to analyse but hard to grasp is Majorana bound states (frequently also
called Majorana fermions). Consider a combination of simple ingredients. Take
conventional superconductors, known for almost a century, and understood
extremely well for half a century. Add a semiconducting quantum wire, a basis
of modern electronics, but scaled down; these were studied for decades. The
amazing thing is that the theoretical and experimental progress showed how
combining these two ingredients one can create the special Majorana bound
states. Sergey Frolov very properly
calls them zen particles, by comparison with the god particle, Higgs
boson. They have no energy, no charge, and no mass (which makes them extremely
hard to find), and they store quantum information in a way completely hidden
from environment. The state of these quantum degrees of freedom changes when
they are moved around each other, allowing to implement an alternative route to
quantum computation.

**Topological insulators.** Symmetry has always been a guiding concept in
physics, allowing to generalize conclusions from one particular system to many
which possess similar qualities. The other concept with applicability that is
perhaps as broad is topology. It allows to conclude that certain properties of
superficially very different systems must be identical as long as the two
systems can be continuously transformed into one another. Topological
insulators use a combination of both symmetry and topology. The surface of
these materials is guaranteed to be conducting as long as certain symmetry of
the material is unbroken, and as long as bulk stays insulating.

**Kwant**. Numerical simulation of a physical system is a useful and sometimes
irrepleacable tool in various tasks. It can be used as a boost or a check of
the intuition, it may lead to finding an efficient analytical approximation, or
as the last resort in handling the problems that are beyond the reach of
analytics. To make numerical calculations more accessible to the community,
some of our group members have developed the sofware package kwant with their colleagues, which can be used to
numerically solve a broad range of problems in mesoscopic quantum transport.